Das Gupta, who passed away after a massive heart attack, was 56.
BAI general secretary Anup Narang would fill in for Das Gupta till an interim president is appointed.
Das Gupta's term would have ended next year when BAI elections are scheduled.
"We are too shell shocked and sad to think about the next president right now. But as far as the running of the association is concerned the secretary general will do the job till an ExCo is called in the next few days," BAI vice- president TPS Puri said.
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Another BAI official, however, was of the view that the senior most vice-president may take over for the time being before a meeting is called in the next three months.
"Bihar finance minister Abdul Bari Siddiqui may take over being the senior most VP. But things will only be clearer in a few days," the official said.
Das Gupta was serving as the vice-president of the Indian Olympic Association (IOA) and was also the president of Uttar Pradesh Olympic Association.
"Dr Das Gupta was someone who got money into badminton but after his shocking demise, we have to see how things pan out. Badminton is big now after Saina and Sindhu's Olympic medal and there will be struggle for power. There are various groups who will be trying to stake claim," a source said.
The BAI, meanwhile, condoled Das Gupta's death and said the legacy he left behind will inspire them to take badminton to greater heights.
"A great visionary under whose leadership badminton grew leaps and bounds in India, is unfortunately no more amongst us. This sudden loss has come as a shock to the badminton fraternity across the world," Narang said said in a statement of behalf of the sports body.
A former Congress MP, Das Gupta was the Minister of State for Steel in UPA-I.
Narang added in the statement, "The legacy he has left as a former player, administrator and a great visionary, will continue to inspire and guide Badminton Association of India to work and promote the game.
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